Question

What is the fourth term of the expansion of the binomial (2x + 5)^5?

Answer 1

Ok, 1 bionimial theorem coming right up

for a binomial expansion of (a+b)^n
the kth term is
$\left(\begin{array}{ccc}n\\k-1\end{array}\right)a^{n-(r-1)}b^{k-1}$
$\left(\begin{array}{ccc}n\\k-1\end{array}\right)$ means $\frac{n!}{(k-1)!(n-(k-1))!}$

n is 5
4th term
4-1=3
and a=2x
b=5
so
$\left(\begin{array}{ccc}5\\4-1\end{array}\right)(2x)^{5-(4-1)}5^{4-1}$
$\left(\begin{array}{ccc}5\\3\end{array}\right)(2x)^{2}5^{3}$
$\left(\begin{array}{ccc}5\\3\end{array}\right)(2x)^{2}5^{3}$
(10)(4x^2)(125)
5000x^2 is the 4th term